报告题目：Spherical Framelets from Spherical Designs

报告人：庄晓生教授，香港城市大学

报告时间：2026年9月16日（周三）9:00-12:00

报告地点：20-308

报告摘要：In this talk, we discuss the structures of the variational characterization of the spherical t-design, its gradient, and its Hessian in terms of fast spherical harmonic transforms. Moreover, we propose solving the minimization problem of the spherical t-design using the trust-region method to provide spherical t-designs with large values of t. Based on the obtained spherical t-designs, we develop (semi-discrete) spherical tight framelets and their fast spherical framelet transforms for practical spherical signal/image processing. Thanks to the large spherical t-designs and localization property of our spherical framelets, we are able to provide signal/image denoising using local thresholding techniques based on a fine-tuned spherical cap restriction. Many numerical experiments are conducted to demonstrate the efficiency and effectiveness of our spherical framelets and spherical designs, including Wendland function approximation, ETOPO data processing, and spherical image denoising.

报告人简介：庄晓生博士分别于2003年和2005年获中山大学数学学士和硕士学位。2010年获加拿大阿尔伯塔大学应用数学博士学位。2011年及2012年分别于德国奥斯纳布吕克大学与德国柏林工业大学从事博士后研究工作。于2012年开始任职于香港城市大学数学系。现为香港城市大学数学系教授。主要从事应用与计算调和分析、小波分析、信号与图像处理、深度与机器学习等方面的研究。在国际期刊及会议上已发表多篇学术论文与书章，包括Applied and Computational Harmonic Analysis、SIAM Imaging Sciences、AAAI、ICML、JMLR、IEEE TNNLS、IEEE TPAMI等。

邀请人：调和分析及其应用创新团队